Theories of political authority divide naturally into those that locate the source of states' authority in the history of states' interactions with their subjects and those that locate it in structural (or functional) features of states (such as the justice of their basic institutions). This paper argues that purely structuralist theories of political authority (such as those defended by Kant, Rawls, and contemporary "democratic Kantians") must fail because of their inability to solve the boundary problem-namely, the problem of locating the boundaries between different states' domains of authority in the natural or intuitive places.